Extremwertaufgaben: Unterschied zwischen den Versionen

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(Visualisierung zur Überprüfung der Ergebnisse)
(Visualisierung zur Überprüfung der Ergebnisse)
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==Visualisierung zur Überprüfung der Ergebnisse==
 
==Visualisierung zur Überprüfung der Ergebnisse==
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showResetIcon = "false" showAnimationButton = "true" enableRightClick = "false" errorDialogsActive = "true" enableLabelDrags = "false" showMenuBar = "false" showToolBar = "false" showToolBarHelp = "false" showAlgebraInput = "false" useBrowserForJS = "true" allowRescaling = "true" />
+
Bewege den roten Punkt, um die Groesse der Schachtel zu verändern
 +
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==Visualisiserung mit Tabelle==
 
==Visualisiserung mit Tabelle==

Version vom 31. Januar 2012, 21:02 Uhr

Inhaltsverzeichnis

Problemstellung

Der Goldfisch in Wermelskirchen möchte wiedereröffnen. Da es sich um einen Raucher-club handeln soll, hat der neue Inhaber sich überlegt, Streichholzschachteln als Werbung zu nutzen. Den Großteil seines Geldes hat er bereits in die Sanierung gesteckt, deshalb will er die Streichholzschachteln von seinen Mitarbeitern basteln lassen und zwar mit möglichst wenig Materialverbrauch. In einem Großmarkt hat der Besitzer dementspre-chend Pappe und Streichhölzer (4,5cm lang) gekauft. Einer der Mitarbeiter kam gestern mit folgender Bastelanleitung zu mir:

(Siehe Aufgabenblatt)

Er fragte mich, wie er aus der Pappe möglichst viele Streichholzschachteln basteln könnte. Als Vorgabe hat er gesagt bekommen, dass das Volumen 45cm³ haben muss. Könnt ihr ihm helfen, herauszufinden, welche Maße die Streichholzschachtel haben muss? (Die Klebekanten [siehe gestrichelte Linien] werden für die Berechnung nicht weiter berücksichtigt)

Falls du nicht weiterkommst: Hier findest du Hilfen

Hauptbedingung

 O=15a+20b+4ab

Nebenbedingung

 45=5ab

Zielfunktion

 O(a)=15a+180/a+36

Ableitung

 O'(a)=15+180/a^2

Notwendige Bedingung

 0=15+180/a^2

 a=3,46cm


Hinreichende Bedingung

 O''(3,46)>0 --> Tiefpunkt

Seitenlänge b und Oberfläche O

 b=2,6cm

 O=139,9cm^2

Randextrema

Sowohl fuer a gegen 0 als auch fuer a gegen unendlich, geht O(a) 
gegen unendlich --> 3,46 ist ein globales Minimum

Visualisierung zur Überprüfung der Ergebnisse

Bewege den roten Punkt, um die Groesse der Schachtel zu verändern

Visualisiserung mit Tabelle

Weiterführende Problemstellung

Bastel eine "optimale" Streichholzschachtel.

Überlege: Warum sind Streichholzschachteln in der Realität nicht "optimal"?

Verfasser

Team.gif
Entstanden unter Mitwirkung von:

Janina Wittenstein